Weak localization with nonlinear bosonic matter waves

[en] We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross–Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.

Disciplines :

Physics

Author, co-author :

Hartmann, Timo

Michl, Josef

Petitjean, Cyril ; Université de Liège - ULiège > Département de physique > Physique quantique statistique

Wellens, Thomas

Urbina, Juan-Diego

Richter, Klaus

Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique

Language :

English

Title :

Weak localization with nonlinear bosonic matter waves

Publication date :

2012

Journal title :

Annals of Physics

ISSN :

0003-4916

eISSN :

1096-035X

Publisher :

Academic Press, San Diego, United States - California

Volume :

327

Pages :

1998-2049

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 27 August 2012

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Dumke R., Müther T., Volk M., Ertmer W., Birkl G. Phys. Rev. Lett. 2002, 89:220402.
Folman R., Krüger P., Cassettari D., Hessmo B., Maier T., Schmiedmayer J. Phys. Rev. Lett. 2000, 84:4749.
Fortágh J., Zimmermann C. Rev. Modern Phys. 2007, 79:235.
Guerin W., Riou J.-F., Gaebler J.P., Josse V., Bouyer P., Aspect A. Phys. Rev. Lett. 2006, 97:200402.
Couvert A., Jeppesen M., Kawalec T., Reinaudi G., Mathevet R., Guéry-Odelin D. EPL 2008, 83:50001.
Fabre C.M., Cheiney P., Gattobigio G.L., Vermersch F., Faure S., Mathevet R., Lahaye T., Guéry-Odelin D. Phys. Rev. Lett. 2011, 107:230401.
Gattobigio G.L., Couvert A., Georgeot B., Guéry-Odelin D. Phys. Rev. Lett. 2011, 107:254104.
Milner V., Hanssen J.L., Campbell W.C., Raizen M.G. Phys. Rev. Lett. 2001, 86:1514.
Friedman N., Kaplan A., Carasso D., Davidson N. Phys. Rev. Lett. 2001, 86:1518.
Henderson K., Ryu C., MacCormick C., Boshier M.G. New J. Phys. 2009, 11:043030.
Billy J., Josse V., Zuo Z., Bernard A., Hambrecht B., Lugan P., Clément D., Sanchez-Palencia L., Bouyer P., Aspect A. Nature 2008, 453:891.
Roati G., D'Errico C., Fallani L., Fattori M., Fort C., Zaccanti M., Modugno G., Modugno M., Inguscio M. Nature 2008, 453:895.
Stibor A., Kraft S., Campey T., Komma D., Günther A., Fortágh J., Vale C.J., Rubinsztein-Dunlop H., Zimmermann C. Phys. Rev. A 2007, 76:033614.
Lin Y.-J., Compton R.L., Perry A.R., Phillips W.D., Porto J.V., Spielman I.B. Phys. Rev. Lett. 2009, 102:130401.
Juzelinas G., Öhberg P., Ruseckas J., Klein A. Phys. Rev. A 2005, 71:053614.
Ruseckas J., Juzelinas G., Öhberg P., Fleischhauer M. Phys. Rev. Lett. 2005, 95:010404.
Dalibard J., Gerbier F., Juzelinas G., Öhberg P. Rev. Modern Phys. 2011, 83:1523.
Altshuler B.L., Khmel'nitzkii D., Larkin A.I., Lee P.A. Phys. Rev. B 1980, 22:5142.
Bergmann G. Phys. Rep. 1984, 107:1.
Van Albada M.P., Lagendijk A. Phys. Rev. Lett. 1985, 55:2692.
Wolf P.-E., Maret G. Phys. Rev. Lett. 1985, 55:2696.
Aronov A.G., Sharvin Y.V. Rev. Modern Phys. 1987, 59:755.
Chang A.M., Baranger H.U., Pfeiffer L.N., West K.W. Phys. Rev. Lett. 1994, 73:2111.
Altshuler B.L., Aronov A.G., Khmelnitsky D.E. J. Phys. C: Solid State Phys. 1982, 15:7367.
Altshuler B.L., Aronov A.G. Electron-Electron Interaction in Disordered Systems 1985, 1. Elsevier, Amsterdam. A.L. Efros, M. Pollak (Eds.).
Whitney R.S., Jacquod P., Petitjean C. Phys. Rev. B 2008, 77:045315.
Hartung M., Wellens T., Müller C.A., Richter K., Schlagheck P. Phys. Rev. Lett. 2008, 101:020603.
Zumbühl D.M., Miller J.B., Marcus C.M., Campman K., Gossard A.C. Phys. Rev. Lett. 2002, 89:276803.
Baranger H.U., Jalabert R.A., Stone A.D. Chaos 1993, 3:665.
Richter K., Sieber M. Phys. Rev. Lett. 2002, 89:206801.
Heusler S., Müller S., Braun P., Haake F. Phys. Rev. Lett. 2006, 96:066804.
Wellens T., Grémaud B. Phys. Rev. Lett. 2008, 100:033902.
Wellens T., Grémaud B. Phys. Rev. A 2009, 80:063827.
Wellens T. Appl. Phys. B 2009, 95:189.
Leboeuf P., Pavloff N. Phys. Rev. A 2001, 64:033602.
Landauer R. IBM J. Res. Dev. 1957, 1:223.
Landauer R. Philos. Mag. 1970, 21:863.
Büttiker M., Imry Y., Landauer R., Pinhas S. Phys. Rev. B 1985, 31:6207.
Dalfovo F., Giorgini S., Pitaevskii L.P., Stringari S. Rev. Modern Phys. 1999, 71:463.
Ernst T., Paul T., Schlagheck P. Phys. Rev. A 2010, 81:013631.
Skipetrov S.E., Maynard R. Phys. Rev. Lett. 2000, 85:736.
Spivak B., Zyuzin A. Phys. Rev. Lett. 2000, 84:1970.
Paul T., Leboeuf P., Pavloff N., Richter K., Schlagheck P. Phys. Rev. A 2005, 72:063621.
Gutzwiller M.C. Chaos in Classical and Quantum Mechanics 1990, Springer, New York.
Jalabert R.A. Proceedings of the International School of Physics "Enrico Fermi" Course CXLIII 2000, p. 145. IOS Press, Amsterdam. G. Casati, I. Guarneri, U. Smilansky (Eds.).
Richter K. Semiclassical Theory of Mesoscopic Quantum Systems 2000, Springer, Heidelberg.
Hannay J.H., Ozorio De Almeida A.M. J. Phys. A: Math. Gen. 1984, 17:3429.
Sieber M. J. Phys. A: Math. Gen. 1999, 32:7679.
Richter K., Ullmo D., Jalabert R.A. Phys. Rev. B 1996, 54:R5219.
Müller S., Heusler S., Braun P., Haake F. New J. Phys. 2007, 9:12.
Sieber M., Richter K. Phys. Scr. 2001, T90:128.
Sieber M. J. Phys. A: Math. Gen. 2002, 35:L613.
Turek M., Richter K. J. Phys. A: Math. Gen. 2003, 36:L455.
Spehner D. J. Phys. A: Math. Gen. 2003, 36:7269.
Müller S., Heusler S., Braun P., Haake F., Altland A. Phys. Rev. E 2005, 72:046207.
Brouwer P.W., Rahav S. Phys. Rev. B 2006, 74:075322.
Waltner D., Gutiérrez M., Goussev A., Richter K. Phys. Rev. Lett. 2008, 101:174101.
Gutiérrez M., Waltner D., Kuipers J., Richter K. Phys. Rev. E 2009, 79:046212.
Paul T., Richter K., Schlagheck P. Phys. Rev. Lett. 2005, 94:020404.
T. Hartmann, J.-D. Urbina, K. Richter, and P. Schlagheck (in preparation).
Ferry D.K., Goodnick S.M. Transport in Nanostructures 1997, Cambridge University Press, Cambridge. first ed.
Datta S. Electronic Transport in Mesoscopic Systems 2007, Cambridge University Press, Cambridge.
Sánchez D., Büttiker M. Phys. Rev. Lett. 2004, 93:106802.
Gusev G.M., Kvon Z.D., Olshanetsky E.B., Plotnikov A.Y. EPL 2009, 88:47007.
F. Eckert, Transport in non-linear disordered media, Master's Thesis, Universität Freiburg, 2010.
Peierls R. Z. Phys. A 1933, 80:763.
Paul T., Hartung M., Richter K., Schlagheck P. Phys. Rev. A 2007, 76:063605.
Lee P.A., Fisher D.S. Phys. Rev. Lett. 1981, 47:882.
Nocedal J., Wright S.J. Numerical Optimization 2006, Springer, Berlin. second ed.
Seydel R. From Equilibrium to Chaos - Practical Bifurcation and Stability Analysis 1988, Elsevier, Amsterdam.
Pethick C.J., Smith H. Bose-Einstein Condensation in Dilute Gases 2002, Cambridge University Press, Cambridge.
Lehoucq R.B., Sorensen D.C., Yang C. ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods 1997, Siam.
Moiseyev N. Phys. Rep. 1998, 302:212-293.
Bohigas O., Giannoni M.-J., Ozorio de Almeida A.M., Schmit C. Nonlinearity 1995, 8:203.
Jensen R.V. Chaos 1991, 1:101.